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Background  Recent approaches mixing frequentist principles with Bayesian inference propose internal goodness-of-fit (GOF) p-values that might be valuable for critical analysis of Bayesian statistical models. However, GOF p-values developed to date only have known probability distributions under restrictive conditions. As a result, no known GOF p-value has a known probability distribution for any discrepancy function.    Methodology/Principal Findings  We show mathematically that a new GOF p-value, called the sampled posterior p-value (SPP), asymptotically has a uniform probability distribution whatever the discrepancy function. In a moderate finite sample context, simulations also showed that the SPP appears stable to relatively uninformative misspecifications of the prior distribution.    Conclusions/Significance  These reasons, together with its numerical simplicity, make the SPP a better canonical GOF p-value than existing GOF p-values.

A New Calibrated Bayesian Internal Goodness-of-Fit Method: Sampled Posterior p-Values as Simple and General p-Values That Allow Double Use of the Data